延性材料中球腔膨胀模型及其解析解的进一步研究

Further Study on Analytical Solution for Spherical Expansion Model in Ductile Media

空腔膨胀模型是当前广泛应用于许多工程领域的一个理论模型。基于Euler坐标构架,对球腔膨胀过程中不同阶段介质内的应力应变场的通解进行理论推导。讨论了当前国内外的一些推导成果的不足之处,分析表明当前的研究结果具有弹塑性解不连续、混淆了弹性体积压缩率和塑性阶段体积压缩率的概念等局限性,是一种间断的特解。给出了考虑塑性压缩性和塑性不可压两种情况下的弹塑性通解,在此基础上给出了考虑初始球腔尺寸和弹性变形等相关参数的准确的、连续的通解;并对塑性阶段压缩率的影响进行分析讨论。经过验证分析,这些通解更加普适,其简化及在特定假设下的特解与当前的国内外研究结果一致,该研究为球腔膨胀模型的应用和深化研究提供一定的参考。

The cavity expansion model is widely used in engineering area.The deficiencies and problem of the corresponding solutions in the published literatures,such as discontinuity between the elastic stage and plastic stage and confusion of some concepts,were analyzed and discussed.The general solutions of the relative size of the plastic zone and field of stress in the Euler coordinate system were deduced,in which the initial cavity size and the elastic deformation prior to the plastic deformation were considered.These solutions are verified that they are continuous and universal and the solutions in the published literatures are the special solutions.It can be referred to in the appllication and further study the cavity expansion model.